Stochastic Homogenization of Level-Set Convex Hamilton–Jacobi Equations

By S. Armstrong, Panagiotis E. Souganidis. 2012

70 citations recorded by the source corpus.

We present a simple new proof for the stochastic homogenization of quasiconvex (levelset convex) Hamilton-Jacobi equations set in stationary ergodic environments. Our approach, which is new even in the convex case, yields more information about the qualitative behavior of the effective nonlinearity.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/6d471ef029cfbee9345862523a17e636ad7c7693

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In Applied Mathematics

1. S. Armstrong
2. Bruno Ziliotto
3. Pierre Cardaliaguet
4. Panagiotis E. Souganidis
5. Charles K. Smart
6. P. J. Graber
7. Zhongwei Shen
8. Daniel Lacker

In Computational Theory and Mathematics

1. S. Armstrong
2. Bruno Ziliotto
3. Pierre Cardaliaguet
4. Panagiotis E. Souganidis
5. Jean-Christophe Mourrat
6. Zhongwei Shen
7. Tuomo Kuusi
8. Felix Otto

In Modeling and Simulation

1. S. Armstrong
2. Bruno Ziliotto
3. Pierre Cardaliaguet
4. Panagiotis E. Souganidis
5. Björn Engquist
6. Russell W. Schwab

Citations in the corpus

• Stochastic Homogenization of Nonconvex Hamilton‐Jacobi Equations: A Counterexample (2015, background): “The first result in the stochastic case was obtained by Souganidis [23] and Rezakhanlou and Tarver [21].”
• Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations (2012, methodology): “ion of the eikonal-type equation H(Du,y,ω) = µ, (A.1) in exterior domains, with µ > H∗, where H∗ is a critical parameter. Most of what follows is well-known and can be found for example in [20] or [4], but we briefly sketch the arguments for the convenience of the reader. Throughout this section, ”